Abstract
We define a gradient operator on random variables defined on the “standard Poisson space” (the sample space of paths which have unit jumps and are constant between their jumps). An “integration by parts” formula shows that the adjoint of that operator extends the usual Poisson stochastic integral. We prove a “Malliavin calculus” type of result, which is closely related to the co-area formula of geometric measure theory.
Supported by an NSF postdoctoral fellowship.
The research was carried out while this author was visiting the Institute for Advanced Study, Princeton NJ, and was supported by a grant from the RCA corporation.
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© 1990 Kluwer Academic Publishers
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Carlen, E.A., Pardoux, E. (1990). Differential Calculus and Integration by Parts on Poisson Space. In: Albeverio, S., Blanchard, P., Testard, D. (eds) Stochastics, Algebra and Analysis in Classical and Quantum Dynamics. Mathematics and Its Applications, vol 59. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-7976-8_5
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DOI: https://doi.org/10.1007/978-94-011-7976-8_5
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